Richard Cockerill admitted Leicester will need to improve in next week's Heineken Cup return fixture against Treviso after their win on Sunday.
Tigers laboured to a 33-25 Pool Three success at Welford Road after leading by 19 points at half-time, but they still claimed a bonus point triumph that closed the gap on group leaders Toulouse.
"We were inaccurate - we went to sleep in the second half," Cockerill said.
"It was a lot closer than we would have liked, but it's job done, it is five points.
"It certainly won't lead us to be complacent next week, so maybe it has done us a favour.
"We will have to be a lot better. Treviso were good, but I don't think we were under any illusions. Two years ago, we nearly lost in Treviso in the first round of the pool stage.
"The players will know they are in for a tough afternoon next week. We have got to go there and try to get five points. Whether that is attainable, we will have to see.
"It was job done today, but no more than that.
"Five points next week would be very helpful, but after today's performance from Treviso, in particular, we need to understand the task ahead for us."
Flanker Julian Salvi's try double underpinned an emphatic first-half display from Leicester, while centre Manu Tuilagi and substitute wing Matt Smith also touched down, with fly-half George Ford kicking four conversions, including the extras to a 17th-minute penalty try.
But it proved far from plain sailing for Leicester as Treviso scored three tries of their own by flanker Dean Budd, prop Lorenzo Cittadini and wing Christian Loamanu, while Alberto Di Bernardo landed two conversions and two penalties.
Treviso finished easily the stronger team, which does not auger well for Leicester ahead of next Saturday's return fixture at Stadio Communale di Monigo.
And they dare not take their eye off the ball to focus on January assignments with the Ospreys and Toulouse, otherwise their quarter-final hopes could be over before then.
If the group goes to form and pedigree, then four-time European champions Toulouse's Welford Road visit next month is likely to decide whether they or Tigers progress as pool winners.
Cockerill, meanwhile, paid tribute to Australian Salvi's display, adding: "He has been very good for us.
"With Ben Woods and Craig Newby both retiring, it left us a little bit short in the seven area, and Julian is a very good player.
Salvi admitted the second period had prompted some "clock-watching" in the Leicester ranks, yet he also backed the Tigers to learn from their latest European experience.
"There was a bit of clock-watching at one stage to see how close they (Treviso) were getting, but we are strong enough and experienced enough as a team to make sure we get the wins, especially at Welford Road," Salvi said.
"You need to give credit where credit is due, and Treviso came out well in the second half. They made us work and started to grind away through the middle.
"Going into the game, we wanted to start well, and we did that, scoring four tries before half-time. We were sitting comfortably in the changing room.
"But we have to make sure when we are up quite a bit on the scoreboard that we keep driving the hammer through."
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